overbook

# overbook - An airline carries airplanes which can hold up...

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mean 20 stdev 5 overage cost \$100 overbook underage \$200 1 2 No-shows #NAME? 3 4 tickets issued #NAME? 5 6 airplane cap 100 7 8 overbook #NAME? 9 10 turned back #NAME? 11 cost of turn-back #NAME? 12 13 empty seats #NAME? 14 cost of empty seats #NAME? 15 16 total cost #NAME? 17 18 19 20 21 22 23 24 critical ratio 0.67 25 26 optimal overbook 22.15 27 28 Optimal tickets sold 122 29 30 31 32 33 34 35 36 37 38 39 40 An airline carries airplanes which can hold up to 100 passengers. The airline wishes to sell more than 100 tickets at \$200 per ticket. Each passenger who has paid for a ticket and shows up after all the seats are assigned is entitled to a full refund plus \$100 compensation. What amount of overbooking is optimal for the airline? Assume that that the number of passengers that won't show up follows Normal distribution with rate of mean 25 and standard deviation of 5. Farid Alizadeh: The optimal value is obtained by using the critical method, and assuming normal distribution with mean 20 and standard deviation of 5

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YASAI Simulation Output Workbook overbook.xls YASAI Version: 2 Sheet airline overbook Use Same Seed? Yes Start Date 11/23/2008 Random Number Seed: 84038.61 Start Time 11:20:38 PM Run Time (h:mm:ss) 0:00:09 Scenarios: 40 Sample Size: 1000 Parameter Scenario tickets issued 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 36 36 37 37 38 38 39 39 40 40
Output Name Scenario Observations Mean Minimum total cost 1 1000 3812.545 941.463 394.120 total cost 2 1000 3612.545 941.463 194.120 total cost 3 1000 3412.553 941.431 2.940 total cost 4 1000 3212.853 940.391 102.940 total cost 5 1000 3013.153 939.445 202.940 total cost 6 1000 2813.453 938.594 17.075 total cost 7 1000 2614.173 936.651 48.253 total cost 8 1000 2415.225 934.055 3.160 total cost 9 1000 2217.254 929.418 12.173 total cost 10 1000 2021.094 921.350 11.017 total cost 11 1000 1827.703 908.759 15.729 total cost 12 1000 1638.227 890.804 2.678 total cost 13 1000 1454.966 865.236 2.018 total cost 14 1000 1280.519 830.596 0.088 total cost 15 1000 1116.665 787.788 3.496 total cost 16 1000 969.349 732.814 0.193 total cost 17 1000 838.623 670.996 2.074 total cost 18 1000 725.917 606.523 1.767 total cost 19 1000 637.059 538.931 0.903 total cost 20 1000 572.037 475.412 0.705 total cost 21 1000 533.389 419.667 0.361 total cost 22 1000 518.407 380.115 1.624 total cost 23 1000 523.760 364.025 0.242 total cost 24 1000 550.422 366.536 1.528 total cost 25 1000 596.643 379.931 0.602 total cost 26 1000 654.983 404.823 0.430 total cost 27 1000 728.002 427.011 1.895 total cost 28 1000 811.752 443.912 1.064 total cost 29 1000 902.082 456.556 0.049 total cost 30 1000 996.888 464.872 5.911 total cost 31 1000 1095.374 467.266 22.465 total cost 32 1000 1194.474 468.958 4.472 total cost 33 1000 1293.992 470.028 41.839 total cost 34 1000 1393.728 470.732 11.786 total cost 35 1000 1493.728 470.732 111.786 total cost 36 1000 1593.728 470.732 211.786 total cost 37 1000 1693.728 470.732 311.786 total cost 38 1000 1793.728 470.732 411.786 total cost 39 1000 1893.728 470.732 511.786 total cost 40 1000 1993.728 470.732 611.786 optimal cost 518.407 optimal strategy 22 Standard Deviation Farid Alizadeh: This is the optimal number of overbooked tickets sold. It matches the number obtained

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matches the number obtained by analytical methods.

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2271.177 2590.264 2815.867 2982.696 3182.604 3341.680 3437.420 3583.636 2071.177 2390.264 2615.867 2782.696 2982.604 3141.680 3237.420 3383.636 1871.177 2190.264 2415.867 2582.696 2782.604 2941.680 3037.420 3183.636 1671.177 1990.264 2215.867 2382.696 2582.604 2741.680 2837.420 2983.636 1471.177 1790.264 2015.867 2182.696 2382.604 2541.680 2637.420 2783.636 1271.177 1590.264 1815.867 1982.696 2182.604 2341.680 2437.420 2583.636 1071.177 1390.264 1615.867 1782.696 1982.604 2141.680 2237.420 2383.636 871.177 1190.264 1415.867 1582.696 1782.604 1941.680 2037.420 2183.636 671.177 990.264 1215.867 1382.696 1582.604 1741.680 1837.420 1983.636 479.424 790.264 1015.867 1182.696 1382.604 1541.680 1637.420 1783.636 305.286 599.245 815.867 982.696 1182.604 1341.680 1437.420 1583.636 194.403 420.804 621.784 785.398 982.604 1141.680 1237.420 1383.636 129.687 300.021 440.815 588.913 784.855 943.264 1037.420 1183.636 101.941 206.190 294.514 435.810 595.634 746.308 839.456 985.760 60.445 142.124 226.869 324.473 446.682 562.880 653.108 789.447 61.859 117.072 192.611 266.245 347.219 421.273 516.203 619.650 57.192 118.569 168.878 216.464 266.154 349.669 416.294 490.783 35.165 87.282 149.568 198.112 251.262 292.866 348.208 421.019 43.357 86.649 121.651 168.077 222.209 267.002 313.645 363.524 37.854 74.676 113.849 157.274 197.959 244.085 285.329 350.535 45.647 77.416 119.904 167.862 207.241 253.387 297.331 337.210 54.956 100.288 139.552 180.521 219.902 263.883 301.181 345.681 48.123 96.205 142.165 187.440 231.332 274.224 319.297 368.358 47.209 93.771 154.069 209.341 267.239 321.795 364.829 410.867 83.178 135.768 184.924 239.042 285.577 352.781 402.363 452.335 65.244 157.544 214.981 266.528 326.933 386.837 460.248 518.018 86.139 164.367 266.824 335.159 386.891 460.529 519.590 581.384 127.814 213.312 315.943 402.413 464.954 534.486 602.733 674.341 175.576 285.128 382.549 495.708 557.513 630.257 701.215 771.368 246.229 379.651 481.898 591.124 655.378 729.004 798.765 870.814 340.128 477.215 578.215 690.413 754.987 826.924 898.765 970.814 437.400 575.743 678.215 790.413 854.987 926.924 998.765 1070.814 537.400 675.743 778.215 890.413 954.987 1026.924 1098.765 1170.814 637.400 775.743 878.215 990.413 1054.987 1126.924 1198.765 1270.814 737.400 875.743 978.215 1090.413 1154.987 1226.924 1298.765
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